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Design an amplifier for maximum gain at 4 GHz. Calculate and plot the input return loss and the gain from 3 to 5 GHz. The GaAs FET has the following S parameters (Zo=50 )
)(GHzf11S 21S 12S 22S
0.3
0.4
0.5
o8980.0 o11672.0 o14266.0
o9986.2 o7660.2 o5439.2
o5603.0 o5703.0 o6203.0
o4176.0 o5473.0 o6872.0
Solution:
Check the stability of the transistor by calculating and K at GHz
Constant gain circles and design for specified gain
• To improve bandwidth one should design for a gain less than the maximum obtainable gain.
• Impedance mismatches are purposely introduced to reduce the maximum gains.
• This can be done by plotting constant gain circles on smith chart to represent loci of s and L that give fixed values of gain for the input and output sections (Gs and GL).
• For simplicity consider the unilateral case (S12 is very small)
22
1
1
1
1
UG
G
U TU
T
2
22
2
11
22211211
11 SS
SSSSU
(unilateral figure of merit)
An error of a few tenths of a dB or less will justify the unilateral assumption
Design an amplifier to have a gain of 11 dB at 4.0 GHz. Plot the constant gain circles for Gs=2 dB and 3 dB, and GL = 0 dB and 1 dB. Calculate and plot the input return loss and overall amplifier gain from 3 to 5 GHz. Use an FET with the following S parameters (Zo= 50 ).
)(GHzf 11S 21S 12S22S
3
4
5
o908.0 o12075.0 o14071.0
o1008.2 o805.2 o603.2
0 o5066.0
0 o7060.0
0 o8558.0
Solution
012 Ssince Unilateral Case 111 S 122 S & Unconditionally Stable
• In receiver applications it is often required to have a preamplifier with a low noise figure as possible since the first stage of a receiver front end usually has the dominant effect on the noise performance of the overall system.
• It is not possible to obtain both minimum noise figure and maximum gain for an amplifier, a compromise must be made.
• This can be done by using constant gain circles and circles of constant noise figure to select a usable trade-off between noise figure and gain.
sss jBGY = source admittance presented to transistor.
optY = optimum source admittance that results in minimum noise figure.
minF = minimum noise figure of transistor, obtained when Ys=Yopt
NR = equivalent noise resistance of transistor.
SG = real part of source admittance
s
s
o
sZ
Y
1
11
opt
opt
o
optZ
Y
1
11
Nopt RF ,,min are characteristics of the particular transistor being used, and are called the noise parameters of the device. They are either given by manufacturer, or measured.
A GaAs FET is biased for minimum noise figure and has the following S-parameters and noise parameters at 4 GHz (Z0=50 ); S11=0.6/-60o,
S12=0.05/26o, S21=1.9/81o, S22=0.5/-60o; Fmin=1.6 dB, opt=0.62/100o, RN=20 . For design purposes, assume the device is unilateral, and calculate the maximum error in GT resulting from this assumption. Then design an amplifier having a 2.0 dB noise figure with the maximum gain that is possible with this noise figure.